The publicity regarding the 18-month closure of London's Millennium Bridge due to excessive lateral vibration response under crowd loading during its opening ceremony has highlighted the necessity for further investigation into the sources of this problem. Current design guidelines focus on single pedestrian dynamic loading and subsequently underestimate the dynamic response associated with crowd loading in the design of pedestrian bridges. This deficiency is addressed in this paper with the mathematical incorporation of random crowd effects into the dynamic analysis procedure. The introduction of a crowd factor (Cf) allows the individual response to be extended to incorporate multiple pedestrians with random arrival times. A subsequent statistical analysis into the mean, variance and distribution shape of Cf allowed the mathematical derivation of an equation stipulating its maximum upper value for a deemed appropriate level of confidence.